A-LevelMathematicsProbability and statistics9709/52 · Feb/Mar 2023 · Q36 Marks

80% of the residents of Kinwawa are in favour of a leisure centre being built in the town. 20 residents of Kinwawa are chosen at random and asked, in turn, whether they are in favour of the leisure centre.

(a)Find the probability that more than 17 of these residents are in favour of the leisure centre.[3]
(b)Find the probability that the 5th person asked is the first person who is not in favour of the leisure centre.[1]
(c)Find the probability that the 7th person asked is the second person who is not in favour of the leisure centre.[2]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2023). The mark or mark type is shown in brackets.

[M1] One term 20Cx (p)ˣ (1-p)²⁰⁻ˣ, 0<p<1,0<x<20.
[A1] Correct expression, accept unsimplified, no terms omitted leading to final answer.
[B1] Mark the final answer at the most accurate value 0.206 ≤ p ≤ 0.2061.
[B1] (0.8)⁴ (0.2) = 0.08192, 256/3125 OE. Accept 8192/100000 OE.
[M1] (0.8)⁵ (0.2)²×k or (0.8)⁵ (0.2)×k×0.2, 2 ≤ k ≤ 7.
[A1] 0.0786 < p < 0.07865, 786432/10000000. If A0 awarded, SC B1 for correct answer WWW.

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